DSE M2 Past Papers: Step-by-Step Solutions with Video, 2012–2022
SketchMath explains 45 questions from the 2012–2022 DSE M2 papers with a worked solution and a short GeoGebra animation each. They are the questions where a picture does most of the explaining: curve sketching and tangents, areas and volumes of revolution, rates of change and optimisation, and 3D vectors. The table further down lists every question by year and topic.
Why watch a video for an M2 past paper question?
A marking scheme tells you what to write; it rarely shows why. In M2 the "why" is usually a picture: which curve is on top in an area question, what the solid looks like before you set up π∫y² dx, where the perpendicular from a point meets a plane. Each animation here is a real GeoGebra construction of the question's own numbers, so the picture and the working always agree — and you can open it in SketchMath to drag a point or rotate the solid yourself.
The questions are described in our own words with the same data as the papers. The HKDSE papers are the copyright of the HKEAA and are not reproduced here; the solutions are SketchMath's own, not the official marking scheme.
DSE M2 past paper questions by year and topic
| Year | Curve sketching, tangents and inflexion | Rates of change and optimisation | Areas and volumes of revolution | Vectors |
|---|---|---|---|---|
| 2022 | Q4 points of inflexion | Q7 area cut off by a tangent | Q9 volume about y = 10 | Q12 incentre by vectors |
| 2021 | Q5 rational curve | Q10 shortest distance | Q6 area bounded by a normal Q7 volume of revolution | Q12 tetrahedron |
| 2020 | Q7 tangent from an external point | Q6 related rates | Q9 curve and area | Q12 angle between two planes |
| 2019 | Q8 increasing function | Q3 draining vessel | Q9 common tangent and area | Q12 pyramid |
| 2018 | Q5 curve from its slope Q8 inflexion | Q9 greatest area | Q10 volume of revolution | Q12 projection on a plane |
| 2017 | Q8 curve y = (ln x)² − 2 | Q6 water in a cone | Q9 rational curve and volume | — |
| 2016 | — | Q3 related rate | Q7 volume about the y-axis Q9 cubic and tangent | Q12 line–plane angle |
| 2015 | — | — | Q9 rational curve and area Q12 cup formed by revolution | Q10 tetrahedron |
| 2014 | Q3 implicit tangent | Q10 shortest ladder | Q6 area Q13 volume about the y-axis | Q8 tetrahedron |
| 2013 | Q4 curve from its slope Q5 curve sketching | — | Q6 area and volume | Q10 concyclic points |
| 2012 | Q5 rational curve | Q6 water in a frustum | Q9 volume of revolution | Q7 parallelepiped |
| 45 in total | 11 questions | 9 questions | 15 questions | 10 questions |